The move comes one day after Woodruff made his first start of the season Friday night. Woodruff allowed four hits and two earned runs in 3 2/3 innings in a 5-4 win over the Chicago Cubs. On the year, Woodruff owns a 5.14 ERA in seven innings pitched (three appearances).
Hoover signed a minor-league deal with the Brewers in January. The 30-year-old spent last year with the Arizona Diamondbacks and earned a 3-1 record, 3.92 ERA and a career-best 11.8 K/9 in 41 1/3 innings.
To make room for Hoover on the 40-man roster, Milwaukee designated left-handed pitcher Tyler Webb for assignment.